44ed7/3

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44ed7/3

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Prime factorization	22 × 11
Step size	33.338¢
Octave	36\44ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth	57\44ed7/3 (1900.26¢)
Consistency limit	8
Distinct consistency limit	4

44 equal divisions of 7/3 (abbreviated 44ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 44 equal parts of about 33.3⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/44, or the 44th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	33.3
2	66.7	27/26, 28/27, 29/28
3	100	17/16, 18/17, 19/18
4	133.4	13/12, 14/13
5	166.7	11/10
6	200	9/8
7	233.4	8/7, 31/27
8	266.7	7/6
9	300	19/16, 31/26
10	333.4	17/14, 23/19, 29/24
11	366.7	21/17, 26/21
12	400.1	24/19, 29/23
13	433.4	9/7
14	466.7	17/13, 21/16
15	500.1	4/3
16	533.4	15/11, 19/14
17	566.7	18/13
18	600.1	17/12, 24/17
19	633.4	13/9, 23/16
20	666.8	22/15, 28/19
21	700.1	3/2
22	733.4	26/17, 29/19
23	766.8	14/9
24	800.1	19/12, 27/17
25	833.4	21/13
26	866.8	28/17
27	900.1	27/16
28	933.5	12/7
29	966.8	7/4
30	1000.1	16/9
31	1033.5	20/11, 29/16
32	1066.8	13/7, 24/13
33	1100.2	17/9
34	1133.5	27/14
35	1166.8
36	1200.2	2/1
37	1233.5
38	1266.8	27/13, 29/14
39	1300.2	17/8
40	1333.5	13/6, 28/13
41	1366.9	11/5
42	1400.2	9/4
43	1433.5	16/7
44	1466.9	7/3

Harmonics

Approximation of harmonics in 44ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.2	-1.7	+0.3	+14.1	-1.5	-1.7	+0.5	-3.4	+14.2	+15.9	-1.4
	Relative (%)	+0.5	-5.1	+1.0	+42.2	-4.6	-5.1	+1.5	-10.1	+42.7	+47.8	-4.1
Steps (reduced)		36 (36)	57 (13)	72 (28)	84 (40)	93 (5)	101 (13)	108 (20)	114 (26)	120 (32)	125 (37)	129 (41)

Approximation of harmonics in 44ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.6	-1.5	+12.4	+0.7	-4.3	-3.2	+3.2	+14.4	-3.4	+16.1	+5.8
	Relative (%)	-19.7	-4.6	+37.2	+2.0	-12.8	-9.6	+9.6	+43.2	-10.1	+48.3	+17.4
Steps (reduced)		133 (1)	137 (5)	141 (9)	144 (12)	147 (15)	150 (18)	153 (21)	156 (24)	158 (26)	161 (29)	163 (31)